Symmetry-protected coherent relaxation of open quantum systems.
We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a N\'eel quench. Thanks to a combination of symmetries, the unitary dynamics are preserved up to a single exponential damping factor for sufficiently weak system-bath coupling. This surprising result, confirmed by numerical simulations, can easily be generalized to other many-body open quantum systems. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum of $\hat{\mathcal{L}}$ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.
Publisher URL: http://arxiv.org/abs/1802.05293
DOI: arXiv:1802.05293v1
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